Decentralized Optimization over Tree Graphs

TL;DR

This paper introduces a decentralized algorithm for non-convex optimization over tree networks, enabling nodes to optimize locally and communicate efficiently without synchronization or central control.

Contribution

It proposes a novel multi-sweep communication protocol allowing decentralized, asynchronous optimization on tree-structured networks without requiring global topology knowledge.

Findings

Achieves locally quadratic convergence under certain conditions

Effective in a radial AC power network case study

Nodes do not need to know the entire network topology

Abstract

This paper presents a decentralized algorithm for non-convex optimization over tree-structured networks. We assume that each node of this network can solve small-scale optimization problems and communicate approximate value functions with its neighbors based on a novel multi-sweep communication protocol. In contrast to existing parallelizable optimization algorithms for non-convex optimization the nodes of the network are neither synchronized nor assign any central entity. None of the nodes needs to know the whole topology of the network, but all nodes know that the network is tree-structured. We discuss conditions under which locally quadratic convergence rates can be achieved. The method is illustrated by running the decentralized asynchronous multi-sweep protocol on a radial AC power network case study.